1. Field of the Invention
The field of the invention is that of solid-state laser gyros used for measuring rotation speeds. This type of equipment is used especially for aeronautical applications.
The laser gyro, developed some thirty years ago, is widely used on a commercial scale at the present time. Its principle of operation is based on the Sagnac effect, which induces a frequency difference Δν between the two optical transmission modes that propagate in opposite directions, called counterpropagating modes, of a bidirectional laser ring cavity undergoing a rotational motion. Conventionally, the frequency difference Δν is equal to:Δν=4 AΩ/λL where: L and A are the length and the area of the cavity, respectively; λ is the laser emission wavelength excluding the Sagnac effect; and Ω is the rotation speed of the assembly.
The value of Δν measured by spectral analysis of the beat of the two emitted beams is used to determine the value of Ω very accurately.
2. Description of the Prior Art
It has also been demonstrated that the laser gyro operates correctly only above a certain rotation speed needed to reduce the influence of intermodal coupling. The rotation speed range lying below this limit is conventionally called the blind zone.
The condition for observing the beat, and therefore for the operation of the laser gyro, is the stability and relative equality of the intensities emitted in the two directions. This is not a priori an easy thing to achieve because of the intermodal competition phenomenon, which means that one of the two counterpropagating modes may have a tendency to monopolize the available gain, to the detriment of the other mode.
This problem is solved in standard laser gyros by the use of a gaseous amplifying medium, generally a helium/neon mixture operating at room temperature. The gain curve of the gas mixture exhibits Doppler broadening due to the thermal agitation of the atoms. The only atoms capable of delivering gain to a given frequency mode are thus those whose velocity induces a Doppler shift in the transition frequency, which brings the atom to resonance with the mode in question. Forcing the laser emission to take place other than at the center of the gain curve (by piezoelectric adjustment of the optical path length) ensures that the atoms at resonance with the cavity have a non-zero velocity. Thus, the atoms that can contribute to the gain in one of the two directions have velocities opposite those of the atoms that can contribute to the gain in the opposite direction. The system therefore behaves as if there were two independent amplifying media, one for each direction. Since intermodal competition has thus disappeared, stable and balanced bidirectional emission occurs (in practice, to alleviate other problems, a mixture consisting of two different neon isotopes is used).
However, the gaseous nature of the amplifying medium is a source of technical complications when producing the laser gyro (especially because of the high gas purity required) and of premature wear during use (gas leakage, deterioration of the electrodes, high voltage used to establish the population inversion, etc.).
At the present time, it is possible to produce a solid-state laser gyro operating in the visible or the near infrared using, for example, an amplifying medium based on neodymium-doped YAG (yttrium aluminum garnet) crystals instead of the helium/neon gas mixture, the optical pumping then being provided by diode lasers operating in the near infrared. It is also possible to use, as amplifying medium, a semiconductor material, a crystalline matrix or a glass doped with ions belonging to the class of rare earths (erbium, ytterbium, etc.). Thus, all the problems inherent with the gaseous state of the amplifying medium are de facto eliminated. However, such a construction is made very difficult to achieve due to the homogeneous character of the broadening of the gain curve of the solid-state media, which induces very strong intermodal competition, and because of the existence of a large number of different operating regimes, among which the intensity-balanced bidirectional regime, called the “beat regime”, is one very unstable particular case (N. Kravtsov and E. Lariotsev, “Self-modulation oscillations and relaxations processes in solid-state ring lasers”, Quantum Electronics 24(10), 841-856 (1994)). This major physical obstacle has greatly limited hitherto the development of solid-state laser gyros.
To alleviate this drawback, one technical solution consists in attenuating the effects of the competition between counterpropagating modes in a solid-state ring laser by introducing optical losses into the cavity that depend on the direction of propagation of the optical mode and on its intensity. The principle is to modulate these losses by a feedback device according to the difference in intensity between the two transmitted modes in order to favor the weaker mode to the detriment of the other, so as constantly to slave the intensity of the two counterpropagating modes to a common value.
In 1984, a feedback device was proposed in which the losses were obtained by means of an optical assembly essentially composed of an element exhibiting a variable Faraday effect and of a polarizing element (A. V. Dotsenko and E. G. Lariontsev, “Use of a feedback circuit for the improvement of the characteristics of a solid-state ring laser”, Soviet Journal of Quantum Electronics 14(1), 117-118 (1984) and A. V. Dotsenko, L. S. Komienko, N. V. Kravtsov, E. G. Lariontsev, O. E. Nanii and A. N. Shelaev, “Use of a feedback loop for the stabilization of a beat regime in a solid-state ring laser”, Soviet Journal of Quantum Electronics 16(1), 58-63 (1986)).
The principle of this feedback device is illustrated in FIG. 1. It consists in introducing, into a ring cavity 1 consisting of three mirrors 11, 12 and 13 and an amplifying medium 19, an optical assembly placed in the path of the counterpropagating optical modes 5 and 6, said assembly consisting of a polarizing element 71 and an optical rod 72 exhibiting the Faraday effect, wound with an induction coil 73. At the output of the cavity 1, the two optical modes 5 and 6 are sent to a measurement photodiode 3. One portion of these beams 5 and 6 is taken off by means of the two semireflecting plates 43 and sent to the two photodetectors 42. The signals output by these two photodetectors are representative of the light intensity of the two counterpropagating optical modes 5 and 6. Said signals are sent to an electronic feedback module 4, which generates an electric current proportional to the difference in light intensity between the two optical modes. This electric current determines the value of the losses inflicted at each of the counterpropagating modes 5 and 6. If one of the beams has a higher light intensity than the other, its intensity will be attenuated more, so as to bring the output beams to the same intensity level. Thus, the bidirectional regime is intensity-stabilized.
A solid-state laser gyro can operate, according to this principle, only if the parameters of the feedback device are matched to the dynamics of the system. In order for the feedback device to be able to give correct results, three conditions must be fulfilled:                the additional losses introduced into the cavity by the feedback device must be of the same order of magnitude as the intrinsic losses in the cavity;        the reaction rate of the feedback device must be greater than the rate of variation of the intensities of the emitted modes so that the feedback operates satisfactorily; and        finally, the feedback strength of the feedback device must be sufficient for the effect induced in the cavity to effectively compensate for the intensity variations.        
The Maxwell-Bloch equations are used to determine the complex amplitudes E1,2 of the fields of the counterpropagating optical modes, and also the population inversion density N. These are obtained using a semi-conventional model (N. Kravtsov and E. Lariotsev, “Self-modulation oscillations and relaxations processes in solid-state ring lasers”, Quantum Electronics 24(10), 841-856 (1994)).
These equations are:
                                          ⅆ                          E                              1                ,                2                                              /                      ⅆ            t                          =                                            -                              (                                                      ω                    /                    2                                    ⁢                                      Q                                          1                      ,                      2                                                                      )                                      ⁢                          E                              1                ,                2                                              +                                                    i                ⁡                                  (                                                            m                                              1                        ,                        2                                                              /                    2                                    )                                            ⁢                              E                                  2                  ,                  1                                                      ±                                          i                ⁡                                  (                                      Δ                    ⁢                                                                                  ⁢                                          v                      /                      2                                                        )                                            ⁢                              E                                  1                  ,                  2                                                              +                                    (                                                σ                  /                  2                                ⁢                                                                  ⁢                T                            )                        ⁢                          (                                                                    E                                          1                      ,                      2                                                        ⁢                                                            ∫                      l                                        ⁢                                          N                      ⁢                                                                                          ⁢                                              ⅆ                        x                                                                                            +                                                      E                                          2                      ,                      1                                                        ⁢                                                            ∫                      l                                        ⁢                                                                  Ne                                                                              ±                            2                                                    ⁢                          ikx                                                                    ⁢                                                                                          ⁢                                              ⅆ                        x                                                                                                        )                                                          Equation        ⁢                                  ⁢        1                                                      ⅆ            N                    /                      ⅆ            t                          =                  W          -                      (                          N              /                              T                1                                      )                    -                                    (                              a                /                                  T                  1                                            )                        ⁢            N            ⁢                                                                                                                      E                      1                                        ⁢                                          ⅇ                                                                        -                          ⅈ                                                ⁢                                                                                                  ⁢                        kx                                                                              +                                                            E                      2                                        ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kx                                                                                                                        2                                                          Equation        ⁢                                  ⁢        2            where:                the indices 1 and 2 are representative of the two counterpropagating optical modes;        ω is the laser emission frequency excluding the Sagnac effect;        Q1,2 are the quality factors of the cavity in the two propagation directions;        m1,2 are the backscattering coefficients of the cavity in the two propagation directions;        σ is the effective laser emission cross section;        l is the length of the gain medium traveled;        T=L/c is the transit time of each mode of the cavity;        k=2π/λ is the norm of the wavevector;        W is the pumping rate;        T1 is the lifetime of the excited level; and        a, the saturation parameter, is equal to σT1/8πℏω.        
The right-hand side of equation 1 has four terms. The first term corresponds to the variation in the field due to the losses in the cavity, the second term corresponds to the variation in the field induced by the backscattering of one mode on the other mode in the presence of scattering elements present inside the cavity, the third term corresponds to the variation in the field due to the Sagnac effect, and the fourth term corresponds to the variation in the field due to the presence of the amplifying medium. This fourth term has two components, the first corresponding to the stimulated emission and the second to the backscattering of one mode on the other mode in the presence of a population inversion grating within the amplifying medium.
The right-hand side of equation 2 has three terms, the first term corresponding to the variation in the population inverse density due to the optical pumping, the second term corresponding to the variation in the population inverse density due to the stimulated emission and the third term corresponding to the variation in the population inversion density due to the spontaneous emission.
The mean losses Pc due to the cavity after a complete rotation of the optical mode are consequently:
Pc=ωT/2Q1,2 according to the first term of the right-hand side of equation 1.
The losses introduced by the feedback devices PF must be of the same order of magnitude as these mean losses PC. In general, these losses are of the order of 1 percent.
The reaction rate of the feedback device may be characterized by the bandwidth γ of said feedback device. It has been demonstrated (A. V. Dotsenko and E. G. Lariontsev, “Use of a feedback circuit for the improvement of the characteristics of a solid-state ring laser”, Soviet Journal of Quantum Electronics 14 (1), 117-118 (1984) and A. V. Dotsenko, L. S. Komienko, N. V. Kravtsov, E. G. Lariontsev, O. E. Nanii and A. N. Shelaev, “Use of a feedback loop for the stabilization of a beat regime in a solid-state ring laser”, Soviet Journal of Quantum Electronics 16(1), 58-63 (1986)), using equations 1 and 2, that a sufficient condition for establishing a stable bidirectional regime above the rotation speed can be written as:γ>>ηω/[Q1,2(ΔνT1)2]where η=(W-Wthreshold)/W and η corresponds to the relative pumping rate above the threshold Wthreshold.
To give an example, for a relative pumping rate η of 10%, an optical frequency ω of 18×1014, a quality factor Q1,2 of 107, a frequency difference Δν of 15 kHz and an excited state lifetime T1 of 0.2 ms, the bandwidth y must be greater than 40 kHz.
In order for the loop to operate correctly, the following relationship must also be satisfied:(ΔνT1)2>>1.
Conventionally, the feedback strength q of the feedback device is defined in the following manner:q=[(Q1−Q2)/(Q1+Q2)]/[(I2−I1)/(I2+I1)]where I1 and I2 are the light intensities of the two counterpropagating modes.
In this type of application, it has been demonstrated that the parameter q must be greater than 1/(ΔνT1)2 in order for the feedback device to be able to operate correctly.